When a planet moves around the sun

Options

A. areal velocity is constant
B. linear velocity is constant
C. angular velocity is constant
D. All of the above

Explanation

To solve the question regarding the motion of a planet around the sun, we need to analyze the concepts of aerial velocity, linear velocity, and angular velocity based on Kepler's laws of planetary motion.

### Step-by-Step Solution:

1. **Understanding Kepler's Second Law**:
- Kepler's Second Law states that a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time. This means that the aerial velocity (area swept out per unit time) of the planet is constant.

2. **Defining Aerial Velocity**:
- Aerial velocity can be defined mathematically as:
\[ \text{Aerial Velocity} = \frac{dA}{dt} \]
where \(dA\) is the area swept out and \(dt\) is the time interval. According to Kepler's Second Law, this remains constant.

3. **Linear and Angular Velocity**:
- Linear velocity refers to the speed of the planet along its orbital path, while angular velocity refers to the rate of change of the angle (in radians) that the planet sweeps out in its orbit.
- As the planet moves in an elliptical orbit, both the distance from the sun and the speed of the planet change. Therefore, linear velocity and angular velocity are not constant.

4. **Conclusion**:
- From the analysis, we conclude that:
- Aerial velocity is constant.
- Linear velocity and angular velocity are not constant and change as the planet orbits the sun.
- Therefore, the correct answer to the question is that **aerial velocity is constant**, while linear and angular velocities are variable.

### Final Answer:
- The correct option is: **Aerial velocity is constant**.